An arm length stabilization system for KAGRA and future gravitational-wave detectors

Modern ground-based gravitational wave (GW) detectors require a complex interferometer configuration with multiple coupled optical cavities. Since achieving the resonances of the arm cavities is the most challenging among the lock acquisition processes, the scheme called arm length stabilization (ALS) had been employed for lock acquisition of the arm cavities. We designed a new type of the ALS, which is compatible with the interferometers having long arms like the next generation GW detectors. The features of the new ALS are that the control configuration is simpler than those of previous ones and that it is not necessary to lay optical fibers for the ALS along the kilometer-long arms of the detector. Along with simulations of its noise performance, an experimental test of the new ALS was performed utilizing a single arm cavity of KAGRA. This paper presents the first results of the test where we demonstrated that lock acquisition of the arm cavity was achieved using the new ALS. We also demonstrated that the root mean square of residual noise was measured to be 8.2 Hz in units of frequency, which is smaller than the linewidth of the arm cavity and thus low enough to lock the full interferometer of KAGRA in a repeatable and reliable manner

A Hardy's Uncertainty Principle Lemma in Weak Commutation Relations of Heisenberg-Lie Algebra

In this article we consider linear operators satisfying a generalized commutation relation of a type of the Heisenberg-Lie algebra. It is proven that a generalized inequality of the Hardy's uncertainty principle lemma follows. Its applications to time operators and abstract Dirac operators are also investigated

Polar supermultiplets, Hermitian symmetric spaces and hyperkahler metrics

We address the construction of four-dimensional N=2 supersymmetric nonlinear sigma models on tangent bundles of arbitrary Hermitian symmetric spaces starting from projective superspace. Using a systematic way of solving the (infinite number of) auxiliary field equations along with the requirement of supersymmetry, we are able to derive a closed form for the Lagrangian on the tangent bundle and to dualize it to give the hyperkahler potential on the cotangent bundle. As an application, the case of the exceptional symmetric space E_6/SO(10) \times U(1) is explicitly worked out for the first time.Comment: 17 page

Occupation probability of harmonic-oscillator quanta for microscopic cluster-model wave functions

We present a new and simple method of calculating the occupation probability of the number of total harmonic-oscillator quanta for a microscopic cluster-model wave function. Examples of applications are given to the recent calculations including $\alpha+n+n$-model for $^6$He, $\alpha+t+n+n$-model for $^9$Li, and $\alpha+\alpha+n$-model for $^9$Be as well as the classical calculations of $\alpha+p+n$-model for $^6$Li and $\alpha+\alpha+\alpha$-model for $^{12}$C. The analysis is found to be useful for quantifying the amount of excitations across the major shell as well as the degree of clustering. The origin of the antistretching effect is discussed.Comment: 9 page

Femtosecond laser nanostructuring of transparent materials: from bulk to fiber lasers

Progress in high power ultra-short pulse lasers has opened new frontiers in the physics of light-matter interactions and laser material processing. Recently there has been considerable interest in the application of femtosecond lasers to writing inside transparent materials and in particular to fabrication of three-dimensional microstructures